Article
Mechanics
Kosuke Suzuki, Takaji Inamuro, Aoi Nakamura, Fuminori Horai, Kuo-Long Pan, Masato Yoshino
Summary: The lattice Boltzmann method (LBM) is a numerical method for incompressible viscous fluid flows that has recently seen more complex collision models to enhance numerical stability. This paper proposes simple extended LBMs with good stability using the lattice kinetic scheme (LKS), which is improved by the linkwise artificial compressibility method (LWACM) to reduce high-order dissipation errors in high Reynolds number flows. The study compares the numerical stability and accuracy of LBM, LKS, LWACM, and improved LKS in simulations of high Reynolds number shear layers and two-phase flows with large density ratios.
Article
Mathematics, Applied
Michal Benes, Igor Pazanin, Marko Radulovic
Summary: This paper focuses on the initial boundary value problem for the micropolar fluid system in nonsmooth domains with mixed boundary conditions, specifically Navier's slip conditions on solid surfaces and Neumann-type boundary conditions on free surfaces. The paper aims to prove the existence, regularity and uniqueness of the solution in distribution spaces.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2022)
Article
Engineering, Multidisciplinary
Mireille El Haddad, Giordano Tierra
Summary: In this work, a thermodynamically consistent model based on phase field theory is derived to represent two-phase flows with different densities. Three linear numerical schemes are introduced to decouple the system computation in an energy-stable manner. Numerical results are presented to demonstrate the validity of the model and the well behavior of the proposed schemes.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2022)
Article
Physics, Fluids & Plasmas
Jun-Jie Huang
Summary: The study presents a simplified method for stabilizing simulations of incompressible viscous flows, with improvements in density diffusion and numerical dissipation, as well as simplification of complex issues in the original method. Through several test cases, the performance of this method and its applicability in various fluid problems are demonstrated.
Article
Mathematics, Applied
Michal Benes, Petr Kucera, Petra Vackova
Summary: This paper investigates the existence and uniqueness of solutions to the initial-boundary-value problem for time-dependent flows of heat-conducting incompressible fluids through a two-dimensional channel. The boundary conditions consist of a do-nothing boundary condition on the outflow and Navier boundary conditions on the solid walls of the channel. A crucial role is played by a priori estimates in the existence analysis, however, the mixed boundary conditions under consideration do not allow us to derive an energy-type estimate of the solution. The objective is to prove the existence and uniqueness of a solution on a sufficiently short time interval for arbitrarily large data.
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
(2023)
Article
Mechanics
Mrityunjoy Mandal, Jahangir Hossain Shaikh
Summary: This paper presents a numerical simulation method for solving the Navier-Stokes equations using isogeometric finite elements and a principle of virtual power-based weak formulation. The method is suitable for weakly viscous incompressible fluids describing steady flow and does not require special treatment of outflow boundary conditions.
Article
Computer Science, Interdisciplinary Applications
Junxiang Yang, Jian Wang, Zhijun Tan, Junseok Kim
Summary: This study focuses on the numerical approximation of incompressible three-component fluids using ternary Cahn-Hilliard equations and Navier-Stokes equations. The proposed second-order time-accurate, linearly implicit-explicit (IMEX) methods effectively handle the nonlinear and coupling terms, while preserving the energy dissipation law. Extensive computational experiments validate the accuracy, energy stability, and efficiency of the proposed method.
COMPUTER PHYSICS COMMUNICATIONS
(2023)
Article
Chemistry, Multidisciplinary
Yuhao Guo, Yan Wang, Qiqi Hao, Tongguang Wang
Summary: An interface-corrected diffuse interface method is proposed for simulating incompressible multiphase flows with large density ratios. The method maintains both mass conservation and interface shapes by introducing an interface correction term and a mass correction term. The method also includes an improved multiphase lattice Boltzmann flux solver, which reduces interface diffusion and ensures control over interface thickness and mass conservation.
APPLIED SCIENCES-BASEL
(2022)
Article
Physics, Mathematical
Yang Liu, Sheng Xu
Summary: The immersed interface method formulates objects in a flow as singular forces and incorporates jump conditions caused by these forces into numerical schemes for flow computation. The method has been extended to handle non-smooth rigid objects with sharp corners in incompressible viscous flows. By representing object boundaries as polygonal curves moving through a fixed Cartesian grid, necessary jump conditions are computed for boundary condition capturing. Tests using canonical flow problems show that the method has second-order accuracy for velocity and first-order accuracy for pressure, demonstrating efficiency and robustness in simulating flows around non-smooth complex objects.
COMMUNICATIONS IN COMPUTATIONAL PHYSICS
(2021)
Article
Mechanics
Alessandro De Rosis, Enatri Enan
Summary: This paper presents a lattice Boltzmann model for the coupled Allen-Cahn-Navier-Stokes equations in three dimensions, solving equations for fluid velocity and order parameter within a general multiple-relaxation-time framework. The model demonstrates good accuracy against nine benchmark tests and successfully simulates different fluid systems.
Article
Mathematics, Applied
Adam Kajzer, Jacek Pozorski
Summary: This article presents an approach to simulate low speed, two-phase interfacial flows using the diffuse-interface method and the conservative Allen-Cahn equation. The method is computationally efficient for treating incompressible flow and conserves mass and momentum. It is easily implemented in existing numerical codes and can be efficiently executed using parallel computing devices.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mechanics
Tao Chen, Tianshu Liu
Summary: Lie derivative is evaluated and interpreted in relation to fundamental surface physical quantities in near-wall incompressible viscous flows, providing insights into boundary vorticity dynamics and near-wall flow physics. The Lie derivatives are found to be directly associated with boundary enstrophy flux and orthogonal pairs of skin friction, surface vorticity, surface enstrophy gradient, and its conjugate vector.
Article
Mathematics, Applied
Shengchuang Chang, Ran Duan
Summary: This article investigates the linear and nonlinear Rayleigh-Taylor instability of the three-dimensional incompressible viscous Navier-Stokes-Quantum equations. The critical number is determined precisely for the linearized problem, and a linear growth solution is constructed using a modified variational method for k < kc. It is shown that c is infinite for a special steady state, indicating that the quantum potential inhibits the instability rather than cutting it off. Based on this unstable linear solution and a priori estimates of the smooth solution to the perturbed problem, the nonlinear instability of density and velocities is established in the sense of Hadamard.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Youyi Zhao
Summary: In this paper, the global well-posedness of the system of incompressible viscous nonresistive magnetohydrodynamics (MHD) fluids in a three-dimensional horizontally infinite slab with finite height is investigated. The analysis is reformulated into Lagrangian coordinates and a new mathematical approach is developed to establish the global well-posedness of the MHD system without requiring nonlinear compatibility conditions on the initial data.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mechanics
Yao Xiao, Zhong Zeng, Liangqi Zhang, Jingzhu Wang, Yiwei Wang, Hao Liu, Chenguang Huang
Summary: In this paper, a spectral element-based phase field method is proposed for solving the Navier-Stokes/Cahn-Hilliard equations for incompressible two-phase flows. The method effectively tackles the challenge posed by the high-order nonlinear term of the Cahn-Hilliard equation by employing the Newton-Raphson method. The decoupling of the Navier-Stokes equations using a time-stepping scheme improves the stability and convergence efficiency for computations with large density and viscosity contrast.